Determining Water Transport Kinetics in Limestone by Dual-Wavelength Cavity Ring-Down Spectroscopy

Water plays a major role in the deterioration of porous building materials such as those widely found in built heritage, influencing many physical, chemical, and biological decay processes. This article details a proof-of-principle study using near-infrared cavity ring-down spectroscopy (CRDS) to monitor the release of water and its artificially enriched isotopologues from small (ca. 25 × 25 × 5 mm) samples of limestone subject to drying by a fixed flow of nitrogen with varying levels of humidity and at room temperature and atmospheric pressure. Under low-humidity conditions, the drying kinetics are consistent with the well-established two-phase drying process exhibited by porous materials, namely, an initial constant drying rate period (phase I) followed by a falling drying rate period (phase II). The water diffusivity during phase II, DII, was measured (for Clipsham limestone) to be 3.0 × 10–9 ± 1 × 10–10 m2 s–1. The CRDS measurements allow spectroscopic determination of the total mass of water released by the sample, and the calculated values are in excellent agreement with gravimetric analysis. Importantly, the selectivity and sensitivity afforded by CRDS allows isotope analysis to be carried out, such that the flux of isotopically labeled water out of the sample can be determined under conditions of humidified flow where there may be a simultaneous ingress of water from the environment. Dual-wavelength CRDS distinguishes isotopic species, and it is demonstrated that the drying kinetics and physical properties of the samples are self-consistent when monitoring both HDO and H2O (for HDO, DII was 3.2 × 10–9 ± 4 × 10–10 m2 s–1). As the humidity levels in the flow increase, a departure from the distinct two-phase behavior is observed in the HDO drying curves. These new measurements of isotopically resolved mass fluxes will help refine models for drying mechanisms in porous media.


Stone samples -Clipsham limestone
This study investigated the use of CRDS to monitor moisture release using Clipsham limestone as the exemplar limestone. Mercury intrusion porosimetry 1 was carried out by the British Geological Survey to characterise the internal structure of the stone, and determine the open porosity of the sample. The pore size distribution is presented in figure S1 and shows that the Clipsham limestone used in this study has a unimodal pore distribution, with a median pore diameter of 1.

Spectroscopic nomenclature
Water is an asymmetric top molecule, with three unique moments of inertia. The rotational levels for water are reported in terms of J, the total angular momentum quantum number, K a , the projection quantum number along the a axis, and K c , the projection quantum number along the c axis. Water has three vibrational modes: ν 1 is the symmetric stretch, ν 2 is the symmetric bend and ν 3 is the asymmetric stretch. The ro-vibrational transitions S2 are reported by the angular momentum and vibrational quantum numbers of the lower and upper levels as the following: The transitions of interest in this work are the: • H 2 O 10,3,7 (021) ← 11,3,8 (000) transition at 6638.91 cm −1 ; • H 2 O 6,0,6(031) ← 7,0,7(010) transition at 6636.57 cm −1 ; • HDO 8,6,2(210) ← 9,6,3(000) transition at 6638.17 cm −1 .

Wavelength calibration
The emission wavelength of the DFB laser is strongly dependent on its temperature and operating current, and in this experiment the fine tuning of the wavelength was made by controlling the laser temperature. Wavelength calibration has been carried out using a Burleigh WA-1000 wavemeter at constant laser drive current of 120 mA. This is shown in figure S2.

Reproducibility
To test the reproducibility of the CRDS measurement, and also variation between samples of the same limestone, the experiment of measuring α p as a function of time with a 1.5 slm dry N 2 flow was repeated with four ca. 25 × 25 × 5 mm Clipsham limestone samples. Figure   S3 shows the normalised mass difference curves for the four samples and table S1 reports their drying kinetics. As expected there are slight variations due to differences between the samples but overall good agreement between the different parameters determined.
S3 Figure S2: Wavelength calibration curve for the 1506 nm DFB laser as a function of temperature, measured at constant current of 120 mA. This was measured using the Burleigh WA-1000 wavemeter and fitted with a fourth order polynomial.